Texturing each object separately VS all in the same texture file
For re-usability sake I would advise texturing and unwrapping each object separately and independently.

That would make it easier to recycle assets for future projects without bringing useless information attached.

You could then reuse only say the Fan and Statue asset in another project easily without bringing the Normal and Specular data of say the Extinguisher and TV and every other object with it, needlessly being loaded into memory and possibly ruining performance of your scene.

It will also make it a lot easier to edit each object separately without having to worry about overlapping the UV space reserved of any other asset, and recalculating UV, or Normals or baking data without having to bake all of them.

If you are absolutely sure this is the final version of your assets, you won't be editing or improving them more in the future, or you plan on always using all or most of the assets at once in all projects then it might be worth the hassle.

If performance or available memory is really a strong concern (say mobile platforms, low end devices, etc.) it may also be worth the trouble of joining them all.

I am not in the game making industry, and this may of course be a bit of a subjective matter, so opinions may vary.

EDIT: An additional concern may be object variations, or like if you want to modify only one single object. 

Say you have a red extinguisher, but now you want a yellow one, or worse want to used both in your scene simultaneously. Now you have to edit the texture with all objects lying around; and if you want to keep both colors you now have two huge duplicated textures, which will have to be loaded entirely into memory just for a small part of one of them.